To comprehend the idea of thermodynamical evolution, we require a heat transport equation derived from the dissipative theory in [1]}-[2]}. The relaxation time denoted as \(\bar{\tau }\)  for the dissipative phenomenon is the most crucial parameter in such theories [3]}. It is delineated as the time consumed by the astrophysical object for getting back to its steady state after being removed from it. Thus, \(\bar{\tau }\)  has its own physical interpretation and if the time scale of the considered system gets smaller or equal to the order of \(\bar{\tau }\) , then neglecting this quantity would amount to the negligence of the whole system.
The heat transport equation reads
\(\nonumber \bar{\tau }h^\rho _\gamma q^\gamma _{;\pi }V^\pi +q^\rho =-\kappa h^{\rho \gamma }(T_{,\gamma }+Ta_\gamma )-\frac{1}{2}\kappa T^2\left(\frac{\bar{\tau } V^\sigma }{\kappa T^2}\right)_{;\sigma }q^\rho ,\) 
